Observations Of Neutron Stars Research Articles

Extracting nuclear symmetry energies at high densities from observations of neutron stars and gravitational waves

By numerically inverting the Tolman-Oppenheimer-Volkov (TOV) equation using an explicitly isospin-dependent parametric Equation of State (EOS) of dense neutron-rich nucleonic matter, a restricted EOS parameter space is established using observational constraints on the radius, maximum mass, tidal polarizability and causality condition of neutron stars (NSs). The constraining band obtained for the pressure as a function of energy (baryon) density is in good agreement with that extracted recently by the LIGO+Virgo Collaborations from their improved analyses of the NS tidal polarizability in GW170817. Rather robust upper and lower boundaries on nuclear symmetry energies are extracted from the observational constraints up to about twice the saturation density $\rho_0$ of nuclear matter. More quantitatively, the symmetry energy at $2\rho_0$ is constrained to $E_{\rm{sym}}(2\rho_0)=46.9\pm10.1$ MeV excluding many existing theoretical predictions scattered between $E_{\rm{sym}}(2\rho_0)=15$ and 100 MeV. Moreover, by studying variations of the causality surface where the speed of sound equals that of light at central densities of the most massive neutron stars within the restricted EOS parameter space, the absolutely maximum mass of neutron stars is found to be 2.40 M$_{\odot}$ approximately independent of the EOSs used. This limiting mass is consistent with findings of several recent analyses and numerical general relativity simulations about the maximum mass of the possible super-massive remanent produced in the immediate aftermath of GW170817.

Strangeness in Neutron Star Cooling

We study the thermal evolution of neutron stars in the presence of hyperons or kaons in the core. Our results indicate that the nucleon and the hyperon direct Urca processes play crucial roles for macroscopic cooling behavior of neutron stars. The presence of hyperons drives fast cooling mechanisms in two ways: 1) it allows the hyperon direct Urca prior to the nucleon direct Urca, and 2) it makes the nucleon direct Urca more feasible by reducing the neutron Fermi momentum. All of the equations of state (EOSs) used in this work satisfy the maximum mass constraints and the allowed areas of mass and radii of neutron stars. We found that the neutron star EOS with hyperons can still be consistent with both mass and temperature observations if the original neutron star’s EOS without hyperons is stiff enough. On the other hand, we found that the neutron star’s EOS with kaons can be consistent only with mass observations, but can hardly explain the cooling behavior if we take into account the statistical distribution of observed neutron star masses.

Tidal deformability and other global parameters of compact stars with strong phase transitions

Context. Using parametric equations of state (relativistic polytropes and a simple quark bag model) to model dense-matter phase transitions, we study global, measurable astrophysical parameters of compact stars such as their allowed radii and tidal deformabilities. We also investigate the influence of stiffness of matter before the onset of the phase transitions on the parameters of the possible exotic dense phase. Aims. The aim of our study is to compare the parameter space of the dense matter equation of state permitting phase transitions to a sub-space compatible with current observational constraints such as the maximum observable mass, tidal deformabilities of neutron star mergers, radii of configurations before the onset of the phase transition, and to give predictions for future observations. Methods. We studied solutions of the Tolman-Oppenheimer-Volkoff equations for a flexible set of parametric equations of state, constructed using a realistic description of neutron-star crust (up to the nuclear saturation density), and relativistic polytropes connected by a density-jump phase transition to a simple bag model description of deconfined quark matter. Results. In order to be consistent with recent observations of massive neutron stars, a compact star with a strong high-mass phase transition cannot have a radius smaller than 12 km in the range of masses 1.2 − 1.6 M⊙. We also compare tidal deformabilities of stars with weak and strong phase transitions with the results of the GW170817 neutron star merger. Specifically, we study characteristic phase transition features in the Λ1 − Λ2 relation, and estimate the deviations of our results from the approximate formulæ for Λ∼ − R (M1) and Λ-compactness proposed in the literature. We find constraints on the hybrid equations of state to produce stable neutron stars on the twin branch. For the exemplary equations of state most of the high-mass twins occur for the minimum values of the density jump λ = 1.33 − 1.54; corresponding values of the square of the speed of sound are α = 0.7 − 0.37. We compare results with observations of gravitational waves and with the theoretical causal limit and find that the minimum radius of a twin branch is between 9.5 and 10.5 km, and depends on the phase transition baryon density. For these solutions the phase transition occurs below 0.56 fm−3.

Neutron stars meet constraints from high and low energy nuclear physics

A novel equation of state used for analysis of the heavy ion collision experimental data is generalized to also describe the matter inside neutron stars. This approach differs from others by including an induced surface tension caused by the short range repulsion between particles accounted by presence of their hard cores. This new equation of state respects thermodynamic consistency and is free from the usual causality problems. This makes it applicable over a wide range of temperatures and baryon densities, including the ones inside neutron stars. Despite small number of parameters the present equation of states reproduces properties of the saturated nuclear matter and is consistent with the proton flow constraint as well as with the results of analysis of the hadron multiplicities measured in heavy ion collisions. It is also consistent with astrophysical data obtained from neutron star observations. Accordingly, we found the set of parameters that agree with the same ones obtained from the heavy ion collision data analysis.

Neutron stars and stellar mergers as a laboratory for dense QCD matter

Neutron star observations, including direct mass and radius measurements as well as the analysis of gravitational wave signals emitted by stellar mergers, provide valuable and unique insights into the properties of strongly interacting matter at high densities. In this proceedings contribution, I review recent efforts to systematically constrain the equation of state (EoS) of dense nuclear and quark matter using a combination of ab initio particle and nuclear physics calculations and astrophysical data. In particular, I discuss the constraints that the gravitational wave observation GW170817 has placed on the EoS, and comment on the future prospects of improving the accuracy, to which this quantity is known.

Diffusive nuclear burning in cooling simulations and application to new temperature data of the Cassiopeia A neutron star

A critical relation in the study of neutron star cooling is the one between surface temperature and interior temperature. This relation is determined by the composition of the neutron star envelope and can be affected by the process of diffusive nuclear burning (DNB), which occurs when elements diffuse to depths where the density and temperature are sufficiently high to ignite nuclear burning. We calculate models of H-He and He-C envelopes that include DNB and obtain analytic temperature relations that can be used in neutron star cooling simulations. We find that DNB can lead to a rapidly changing envelope composition and prevents the build-up of thermally stable hydrogen columns y$_H$ > 10$^{7}$ g cm$^{-2}$, while DNB can make helium envelopes more transparent to heat flux for surface temperatures $T_s$ > 2 $\times 10^6$ K. We perform neutron star cooling simulations in which we evolve temperature and envelope composition, with the latter due to DNB and accretion from the interstellar medium. We find that a time-dependent envelope composition can be relevant for understanding the long-term cooling behaviour of isolated neutron stars. We also report on the latest Chandra observations of the young neutron star in the Cassiopeia A supernova remnant; the resulting 13 temperature measurements over more than 18 years yield a ten-year cooling rate of $\approx$ 2%. Finally, we fit the observed cooling trend of the Cassiopeia A neutron star with a model that includes DNB in the envelope.

From QCD symmetries to nuclei and neutron stars

Global symmetries and symmetry breaking patterns of QCD with light quarks, in particular chiral symmetry, provide basic guidance not only for low-energy hadron physics but also for nuclear forces and the nuclear many-body problem. Recent developments of Chiral Effective Field Theory (ChEFT) applications to nuclear and neutron matter are summarized, with special emphasis on a (nonperturbative) extension using functional renormalization group methods. Topics include: nuclear thermodynamics, extrapolations to dense baryonic matter and constraints from neutron star observables.

NonPrimordial Solar Mass Black Holes.

We propose a mechanism that can convert a sizable fraction of neutron stars into black holes with mass ∼1 M_{⊙}, too light to be produced via stellar evolution. We show that asymmetric fermionic dark matter of mass on the teraelectron volt scale, with attractive self-interaction within the range that alleviates the problems of collisionless cold dark matter, can accumulate in a neutron star and collapse, forming a black hole that converts the rest of the star to a solar mass black hole. We estimate the fraction of neutron stars that can become black holes without contradicting neutron star observations. Such solar mass black holes could be in binary systems, which may be searched for by existing and forthcoming gravitational wave detectors. The (non-)observation of binary mergers of solar mass black holes may thus test the nature of dark matter.

Constraints on the Moment of Inertia of PSR J0737-3039A from GW170817

Abstract Continued observation of PSR J0737-3039, the double pulsar, is expected to yield a precise determination of its primary component’s moment of inertia in the next few years. Since the moment of inertia depends sensitively on the neutron star’s internal structure, such a measurement will constrain the equation of state of ultra-dense matter, which is believed to be universal. Independent equation-of-state constraints have already been established by the gravitational-wave measurement of neutron star tidal deformability in GW170817. Here, using well-known universal relations among neutron star observables, we translate the reported 90% credible bounds on tidal deformability into a direct constraint, , on the moment of inertia of PSR J0737-3039A. Should a future astrophysical measurement of I ⋆ disagree with this prediction, it could indicate a breakdown in the universality of the neutron star equation of state.

Tidal Deformabilities and Radii of Neutron Stars from the Observation of GW170817.

We use gravitational-wave observations of the binary neutron star merger GW170817 to explore the tidal deformabilities and radii of neutron stars. We perform a Bayesian parameter estimation with the source location and distance informed by electromagnetic observations. We also assume that the two stars have the same equation of state; we demonstrate that, for stars with masses comparable to the component masses of GW170817, this is effectively implemented by assuming that the stars' dimensionless tidal deformabilities are determined by the binary's mass ratio q by Λ_{1}/Λ_{2}=q^{6}. We investigate different choices of prior on the component masses of the neutron stars. We find that the tidal deformability and 90% credible interval is Λ[over ˜]=222_{-138}^{+420} for a uniform component mass prior, Λ[over ˜]=245_{-151}^{+453} for a component mass prior informed by radio observations of Galactic double neutron stars, and Λ[over ˜]=233_{-144}^{+448} for a component mass prior informed by radio pulsars. We find a robust measurement of the common areal radius of the neutron stars across all mass priors of 8.9≤R[over ^]≤13.2 km, with a mean value of ⟨R[over ^]⟩=10.8 km. Our results are the first measurement of tidal deformability with a physical constraint on the star's equation of state and place the first lower bounds on the deformability and areal radii of neutron stars using gravitational waves.

Testing Dark Decays of Baryons in Neutron Stars.

The observation of neutron stars with masses greater than one solar mass places severe demands on any exotic neutron decay mode that could explain the discrepancy between beam and bottle measurements of the neutron lifetime. If the neutron can decay to a stable, feebly interacting dark fermion, the maximum possible mass of a neutron star is 0.7M_{⊙}, while all well-measured neutron star masses exceed one M_{⊙}. The existence of 2M_{⊙} neutron stars further indicates that any explanation beyond the standard model for the neutron lifetime puzzle requires dark matter to be part of a multiparticle dark sector with highly constrained interactions. Beyond the neutron lifetime puzzle, our results indicate that neutron stars provide unique and useful probes of GeV-scale dark sectors coupled to the standard model via baryon-number-violating interactions.

The Disk Wind in the Neutron Star Low-mass X-Ray Binary GX 13+1

Abstract We present the analysis of seven Chandra High Energy Transmission Grating Spectrometer and six simultaneous RXTE Proportional Counter Array observations of the persistent neutron star (NS) low-mass X-ray binary GX 13+1 on its normal and horizontal branches. Across nearly 10 years, GX 13+1 is consistently found to be accreting at 50%–70% Eddington, and all observations exhibit multiple narrow, blueshifted absorption features, the signature of a disk wind, despite the association of normal and horizontal branches with jet activity. A single absorber with standard abundances cannot account for all seven major disk wind features, indicating multiple absorption zones may be present. Two or three absorbers can produce all of the absorption features at their observed broadened widths and reveal that multiple kinematic components produce the accretion disk wind signature. Assuming the most ionized absorber reflects the physical conditions closest to the NS, we estimate a wind launching radius of 7 × 1010 cm, for an electron density of 1012 cm−3. This is consistent with the Compton radius and also with a thermally driven wind. Because of the source’s high Eddington fraction, radiation pressure likely facilitates the wind launching.

Combined Constraints on the Equation of State of Dense Neutron-rich Matter from Terrestrial Nuclear Experiments and Observations of Neutron Stars

Abstract Within the parameter space of the equation of state (EOS) of dense neutron-rich matter limited by existing constraints mainly from terrestrial nuclear experiments, we investigate how the neutron star maximum mass M max > 2.01 ± 0.04 M ⊙, radius 10.62 km < R 1.4 < 12.83 km and tidal deformability Λ1.4 ≤ 800 of canonical neutron stars together constrain the EOS of dense neutron-rich nucleonic matter. While the 3D parameter space of K sym (curvature of nuclear symmetry energy), J sym, and J 0 (skewness of the symmetry energy and EOS of symmetric nuclear matter, respectively) is narrowed down significantly by the observational constraints, more data are needed to pin down the individual values of K sym, J sym, and J 0. The J 0 largely controls the maximum mass of neutron stars. While the EOS with J 0 = 0 is sufficiently stiff to support neutron stars as massive as 2.37 M ⊙, supporting the hypothetical ones as massive as 2.74 M ⊙ (composite mass of GW170817) requires J 0 to be larger than its currently known maximum value of about 400 MeV and beyond the causality limit. The upper limit on the tidal deformability of Λ1.4 = 800 from the recent observation of GW170817 is found to provide upper limits on some EOS parameters consistent with but far less restrictive than the existing constraints of other observables studied.

Solving the relativistic inverse stellar problem through gravitational waves observation of binary neutron stars

The LIGO/Virgo Collaboration has recently announced the direct detection of gravitational waves emitted in the coalescence of a neutron star binary. This discovery allows, for the first time, to set new constraints on the behavior of matter at supranuclear density, complementary with those coming from astrophysical observations in the electromagnetic band. In this paper we demonstrate the feasibility of using gravitational signals to solve the relativistic inverse stellar problem, i.e., to reconstruct the parameters of the equation of state (EoS) from measurements of the stellar mass and tidal Love number. We perform Bayesian inference of mock data, based on different models of the star internal composition, modeled through piecewise polytropes. Our analysis shows that the detection of a small number of sources by a network of advanced interferometers would allow to put accurate bounds on the EoS parameters, and to perform a model selection among the realistic equations of state proposed in the literature.

Brightening X-Ray/Optical/Radio Emission of GW170817/SGRB 170817A: Evidence for an Electron–Positron Wind from the Central Engine?

Abstract Recent follow-up observations of the binary neutron star (NS) merging event GW170817/SGRB 170817A reveal that its X-ray/optical/radio emissions are brightening continuously up to ∼100 days post-merger. This late-time brightening is unexpected from the kilonova model or the off-axis top-hat jet model for gamma-ray burst (SGRB) afterglows. In this Letter, by assuming that the merger remnant is a long-lived NS, we propose that the interaction between an electron–positron-pair (e + e −) wind from the central NS and the jet could produce a long-lived reverse shock, from which a new emission component would rise and can interpret current observations well. The magnetic-field-induced ellipticity of the NS is taken to be 4 × 10−5 in our modeling, so that the braking of the NS is mainly through the gravitational wave (GW) radiation rather than the magnetic dipole radiation, and the emission luminosity at early times would not exceed the observational limits. In our scenario, because the peak time of the brightening is roughly equal to the spin-down timescale of the NS, the accurate peak time may help constrain the ellipticity of the remnant NS. We suggest that radio polarization observations of the brightening would help to distinguish our scenario from other scenarios. Future observations on a large sample of short gamma-ray burst afterglows or detections of GW signals from merger remnants would test our scenario.

Vector disformal transformation of cosmological perturbations

We study disformal transformations of cosmological perturbations by vector fields in theories invariant under U(1) gauge transformations. Three types of vector disformal transformations are considered: (i) disformal transformations by a single timelike vector; (ii) disformal transformations by a single spacelike vector; and (iii) disformal transformations by three spacelike vectors. We show that transformations of type (i) do not change either curvature perturbation or gravitational waves; that those of type (ii) do not change curvature perturbation but change gravitational waves; and that those of type (iii) change both curvature perturbation and gravitational waves. Therefore, coupling matter fields to the metric after disformal transformations of type (ii) or (iii) in principle have observable consequences. While the recent multi-messenger observation of binary neutron stars has singled out a proper disformal frame at the present epoch with a high precision, the result of the present paper may thus help distinguishing disformal frames in the early universe.

Evolving ONe WD+He star systems to intermediate-mass binary pulsars

It has been suggested that accretion-induced collapse (AIC) is a non-negligible path for the formation of the observed neutron stars (NSs). An ONe white dwarf (WD) that accretes material from a He star may experience AIC process and eventually produce intermediate-mass binary pulsars (IMBPs), named as the ONe WD+He star scenario. Note that previous studies can only account for part of the observed IMBPs with short orbital periods. In this work, we investigate the evolution of about 900 ONe WD+He star binaries to explore the distribution of IMBPs. We found that the ONe WD+He star scenario could form IMBPs including pulsars with 5-340 ms spin periods and 0.75-1.38 Msun WD companions, in which the orbital periods range from 0.04 to 900 d. Compared with the 20 observed IMBPs, this scenario can cover the parameters of 13 sources in the final orbital period-WD mass plane and the Corbet diagram, most of which has short orbital periods. We found that the ONe WD+He star scenario can explain almost all the observed IMBPs with short orbital periods. This work can well match the observed parameters of PSR J1802-2124 (one of the two precisely observed IMBPs), providing a possible evolutional path for its formation. We also speculate that the compact companion of HD 49798 (a hydrogen depleted sdO6 star) may be not a NS based on the present work.

QCD Equations of State in Hadron–Quark Continuity

The properties of dense matter in quantum chromodynamics (QCD) are delineated through equations of state constrained by the neutron star observations. The two solar mass constraint, the radius constraint of ≃11–13 km, and the causality constraint on the speed of sound, are used to develop the picture of hadron–quark continuity in which hadronic matter continuously transforms into quark matter. A unified equation of state at zero temperature and β-equilibrium is constructed by a phenomenological interpolation between nuclear and quark matter equations of state.

Search for Post-merger Gravitational Waves from the Remnant of the Binary Neutron Star Merger GW170817

Abstract The first observation of a binary neutron star (NS) coalescence by the Advanced LIGO and Advanced Virgo gravitational-wave (GW) detectors offers an unprecedented opportunity to study matter under the most extreme conditions. After such a merger, a compact remnant is left over whose nature depends primarily on the masses of the inspiraling objects and on the equation of state of nuclear matter. This could be either a black hole (BH) or an NS, with the latter being either long-lived or too massive for stability implying delayed collapse to a BH. Here, we present a search for GWs from the remnant of the binary NS merger GW170817 using data from Advanced LIGO and Advanced Virgo. We search for short- (≲1 s) and intermediate-duration (≲500 s) signals, which include GW emission from a hypermassive NS or supramassive NS, respectively. We find no signal from the post-merger remnant. Our derived strain upper limits are more than an order of magnitude larger than those predicted by most models. For short signals, our best upper limit on the root sum square of the GW strain emitted from 1–4 kHz is at 50% detection efficiency. For intermediate-duration signals, our best upper limit at 50% detection efficiency is for a millisecond magnetar model, and for a bar-mode model. These results indicate that post-merger emission from a similar event may be detectable when advanced detectors reach design sensitivity or with next-generation detectors.

Colloquium: Astromaterial science and nuclear pasta

We define `astromaterial science' as the study of materials in astronomical objects that are qualitatively denser than materials on earth. Astromaterials can have unique properties related to their large density, though they may be organized in ways similar to more conventional materials. By analogy to terrestrial materials, we divide our study of astromaterials into hard and soft and discuss one example of each. The hard astromaterial discussed here is a crystalline lattice, such as the Coulomb crystals in the interior of cold white dwarfs and in the crust of neutron stars, while the soft astromaterial is nuclear pasta found in the inner crusts of neutron stars. In particular, we discuss how molecular dynamics simulations have been used to calculate the properties of astromaterials to interpret observations of white dwarfs and neutron stars. Coulomb crystals are studied to understand how compact stars freeze. Their incredible strength may make crust "mountains" on rotating neutron stars a source for gravitational waves that the Laser Interferometer Gravitational-Wave Observatory (LIGO) may detect. Nuclear pasta is expected near the base of the neutron star crust at densities of $10^{14}$ g/cm$^3$. Competition between nuclear attraction and Coulomb repulsion rearranges neutrons and protons into complex non-spherical shapes such as sheets (lasagna) or tubes (spaghetti). Semi-classical molecular dynamics simulations of nuclear pasta have been used to study these phases and calculate their transport properties such as neutrino opacity, thermal conductivity, and electrical conductivity. Observations of neutron stars may be sensitive to these properties, and can be be used to interpret observations of supernova neutrinos, magnetic field decay, and crust cooling of accreting neutron stars. We end by comparing nuclear pasta shapes with some similar shapes seen in biological systems.